Antisite defects formation

Theoretical values for vacancy formation in the silicon and carbon sublattices are AITbsi = 4.93 eV and AlVvc = 2.92 eV, respectively energies of antisite defect formation are AlTsic = 3.2 eV and AlVcsi = 2.9 eV. The experimental value of the carbon vacancy migration energy is 1.2 eV for temperatures 1080-1300 K. 

To illustrate exactly how these mles work, a number of examples follow. In the first, the formation of antisite defects, a simple example that does not involve changes in atom numbers or charges on defects, is described. Secondly, two reactions involving oxides, nickel oxide and cadmium oxide, both of which are nonstoichio-metric, but for opposite reasons, indicate how to deal with a solid-gas interaction... 

Antisite defects can be created via the intermediate formation of a Frenkel defect by the following mles ... 

The creation of antisite defects can occur during crystal growth, when wrong atoms are misplaced on the growing surface. Alternatively, they can be created by internal mechanisms once the crystal is formed, provided that sufficient energy is applied to allow for atom movement. For example, antisite defects can be created via the intermediate formation of a Frenkel defect in the following way ... 

An intrinsic defect is one that is in thermodynamic equilibrium in the crystal. This means that a population of these defects cannot be removed by any forms of physical or chemical processing. Schottky, Frenkel, and antisite defects are the best characterized intrinsic defects. A totally defect-free crystal, if warmed to a temperature that allows a certain degree of atom movement, will adjust to allow for the generation of intrinsic defects. The type of intrinsic defects that form will depend upon the relative formation energies of all of the possibilities. The defect with the lowest formation energy will be present in the greatest numbers. This can change with temperature. 

Antisite defects in the pyrochore structure Er2Ti207 were mentioned previously (Section 1.10). These defects also occur in the nonstoichiometric compound Er2.09Ti194O6.952, which is slightly Er203-rich compared to the stoichiometric parent phase. The formation of the antisite pair is now accompanied by the parallel formation of oxygen vacancies ... 

We should mention that antisite defects may be the most common type for as-grown materials, since both lattice atoms belong to the same column of the periodic table. Recent calculations reported by Bernholc et al [124] predict formation energies as low as 3 eV for both of the antisite defects, Sic and CSi, in cubic SiC. However, theoretical studies [124,125] suggest that both types of isolated antisite defects in 3C-SiC are electrically inactive. 

Wang et al [30], Li and Lin-Chung [22], and Talwar and Feng [23] have calculated the formation energy and the bound electronic states of native defects. Li and Lin-Chung [22] showed that isolated silicon and carbon vacancies and a divacancy complex of Si and C sites induce gap states, while no defect-induced state is found in the energy gap for either the isolated Si or C antisite defects or for the pair of antisite defects in SiC. Kohyama et al [31],... 

Figure 3. Dependence of the As antisite formation energy on the concentration x of Mn acceptors and on the concentration y of the antisite defects. The formation energy for x = 0.04 is used as a reference.

Fig. 3 shows the formation energy of the As antisite defect as a function of (Mn). The curves correspond to various concentrations of the antisite defects. The formation energy for x = 0.04 is used as a reference. The formation energy is in all cases decreasing function of x. It is reduced approximately by 0.01 Ry, if the Mn concentration increases by a few atomic percent. This means that the number of the antisite defects can be considerably enhanced in the presence of Mn. This eflfect may contribute to the self-compensation behavior of (Ga,Mn)As alloys. 

Figure 4. Changes AE " of formation energy of substitutional Mn in (Gai 3 yMn3 Asj)As alloys due to the As antisite defects. 

Fig. 155, p. 334, shows the density of TmxSe at room temperature as a function of x, determined with the buoyancy method, together with theoretical values and calculated for the following defect models 1) vacancies, 2) interstitial defects, 3) antisite defects (Tm occupies both cationic and anionic Schottky vacancies), Kaldis, Fritzler [1, p. 125], [2, p. 83], Fritzler, Kaldis [3], Fritzler et al. [4]. The discontinuity at Tmo.sySe is attributed to the formation of the TmsSe superstructure. The difference between experimental and calculated densities for the compositions Tmo.sySe to Tmi oSe is explained by the increasing number of Schottky vacancy pairs. The existence of both iSchottky pairs and antisite defects is assumed between Tm oSe and Tmi oeSe. Selected numerical values of the experimental density as a function of composition ... 

Because their formation energy is generally lower than that of interstitials, the quenching of a stoichiometric intermetallic compound from high temperature, if fast enough, will give isolated vacancies and antisite defects. 

Experimental Studies of the Formation of Vacancies and Antisite Defects... 

The embedded-atom technique was applied to the study of interstitials in NiAl (Caro and Pedraza, 1991) and NisAl (Caro et al, 1990 Pedraza et al., 1991). In Ni3Al, the enthalpy differences between dumbbell, octahedral, and crowdion Ni interstitial configurations are small, typically 0.1 to 0.2 eV. The <100> Ni-Ni dumbbells in pure Ni planes IE = 3.63 eV) are favored Ni-Al and Al-Al dumbbells have larger formation energies (4.45 and 6.22 eV respectively, which is understandable on the basis of size arguments) and hence convert into Ni-Ni dumbbell + Al i antisite defects. This behavior is very similar to that studied experimentally in CU3AU (see Sections 4 and 7). 

First-principles calculations have also been performed for formation energies of native defects in AIN [8,9], The main conclusions are similar to those for GaN self-interstitials and antisites are high in energy - with the exception of the A1 interstitial in cubic AIN, which is a triple donor and could act as a compensating centre in p-type material. 

If we suppose that the thermal vacancies are Co vacancies Oust like the structural vacancies), then this creation must be accommodated by another type of defect to maintain a constant composition. It is generally proposed that the creation of two thermal vacancies always occurs in combination with the formation of an antisite atom (Co atom on Ga site) this is the triple-defect structure proposed first by Wasilewski (1968). 

As in any semiconductors, point defects affect the electrical and optical properties of ZnO as well. Point defects include native defects (vacancies, interstitials, and antisites), impurities, and defect complexes. The concentration of point defects depends on their formation energies. Van de WaHe et al. [86,87] calculated formation energies and electronic structure of native point defects and hydrogen in ZnO by using the first-principles, plane-wave pseudopotential technique together with the supercell approach. In this theory, the concentration of a defect in a crystal under thermodynamic equilibrium depends upon its formation energy if in the following form ... 

The formation energies of native defects in ZnO have been calculated by several groups of theorists and the results generally agree [86,88-91). The results for oxygen and zinc vacancies, interstitials, and antisites in ZnO are shown in Figure 3.17 for the... 

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